Compass for drawing conic sections.



No. 639,488. 1 Patented 1m. |9,.| a99.-- w. ZIETHEN.

COMPASS FOR DRAWING CUNIG SECTIONS.

(Application filed Juna 10, 1899) (No Model.) 4 Sheets-$heet l.

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' 539,:4.88- Patented Dec. I9, 1899. W. ZIETHEN.

COMPASS FOR DRAWING SONIC SECTIONS.

(Application filed June 10, 1899.)

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W 4M ywaziza Patented Dec. 19, I899.

w. Z IETHEN. COMPASS FOR DRAWING C ONIC SECTIONS.

(Application filed June 10, 1899.)

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No. 639.488. Paitented Dec. l9, I899.

W; ZIETHEN. COMPASS FOR DBAWING'CONIG SECTIONS.

(Appliation filed June 10, 1899,)

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Unwrap STATES XVILHELM ZIETHEN, O

PATENT FFlCEe F BERLIN, GERMANY.

' SPECIFICATI ON formingpart of Letters Patent No. 639,488, datedDecember 19, 1899.

Application filed June 10,1899.

To all whom 732% may concern.-

Be it known that I, WILHELM ZIETHEN, a subject of the King of Prussia,German Emperor, residing at the city of Berlin, Germany, have invented anew and useful Improvement in Compasses for Drawing Conic Section-Linesand for Trisecting Angles, of which the following is a specification.

My invention relates to compasses for drawing conic section-lines andfor trisecting angles; and the object of my invention is to provide sucha combination of parts that by one and the same instrument there can bedrawn at will either an ellipse, a hyperbola, or a parabola, and thetrisection of angles can be performed.

My invention substantially consists of a system of links pivotallyconnected to each other to form a movable rhomb, and the said rhomb isprovided with a diagonal rod passing loosely through a pair of oppositepivots of the same and is pivotally connected with one of the two otherpivots bya guide-rod, a drawing-pen being secured at the crossing-pointof the two rods, movable on either of the same.

I have represented my invention in the accompanying drawings, of whichFigures 1 and 2 are a plan and a side view,. respectively, of theinstrument when used for drawing an elliptic line; Figs. 3 and 4:,similar views when drawing a hyperbola, and Figs. 5 and 6 correspondingviews when drawing a parabola. Fig. 7 is a diagram of my inven' tion,showing the same applied to the trisection of angles 5 and Fig. 8 is aperspective View of the leg F for guidance along a ruler when theinstrument is used for drawinga parabola.

Similar parts are indicated by similar numerals and letters throughoutthe several views.

Referring to Figs. 1 and 2, a system of links a b c h are pivotallyconnected to each other at cl 6 f 9, so as to form a movable rhomb. Arod it passes through pivots e and g and a stud o is movably mounted onrod n. Another rod 1' is provided, passing loosely through stud v andpassing likewise through pivot-stud d and a center stud f. Rod '22. isfirmly connected to stud g by a clampingscrew and passes loosely throughstud 0, while rod 7 is firmly connected by clamping-screws to both ofthe studs 01 and f. Studs f and Serial No. 720.076. (N0 model.)

f are provided with points, as appearing from Fig. 2, in order to befixed in the drawingplan and to adjust the instrument for its work, apin projection a: of stud d serving atthe same time as a movable supportof the rhomb, opposite to stud f. A drawing pen or pencil p is securedto stud 'u in contact with the drawing-surface.

In the position of parts represented in Fig. 1 the instrument isadjusted to draw with the pencil an ellipse, the focuses of which areindicated by the fixed pointsfand f, the constant sum of the radiivectors being represented by the fixed distance from point f to point d,firmly connected to each other by the clamped rod 1. If now rod r isgiven a rotary movement around pointf, pencil n will draw a curved line,and as in any position of the pencil the distance between points f and pconstantly equals that between points" 29 and d, fg cl 6 being a rhomb,and point 19 placed on its diagonal line, the curved line drawn by thepencil is characterized by that for each of its points the distance sumfrom two fixed points is a constant quantity-*that is to say, the saidcurved line is an ellipse.

In the position of parts represented in Figs. Sand 4=-that is to say,point (1 being placed between the fixed pointsfandf--the instrument isadjusted to draw a hyperbola, the focuses again being indicated byf andf and the constant diiference of the radii vectors again represented bythe fixed distance f d. For the distance, 12 d always equaling that p f,for the abovementioned reason, the curved line drawn by the pencil 29 atthe r0 tary movement of rod 0" will be characterized by that for each ofits points, the distance difference from two fixed points is a constantquantity-that is to say, the said curved line is a hyperbola,with thefocuses atfandf. Figs. 5 and 6 show my invention adjusted to draw aparabola with the focus at f and the directrix represented by a rule S.In this case the pivot-legs f and (l shown in the preceding figures areremoved and the leg shown in Fig. 8 is substituted,which consists of apost having a perforation 2, into which one end of the rod '1 is securedby means of the thumb-screw 3. The foot of this post has a flange 4:,which guides it along the ruler S, and is provided with a perforation S,into which the pivot d is placed,whichlattersubstitutes the pivot (Z,while the rod f is rigidly held by the thumb-screw 3, so as toconstantly keep rod 0'- in a perpendicular direction with respect to therule. If now pivot- Stud (1 is shifted along rule S, pencil 1) will drawa curved line characterized by that for each of its points the distancefrom a fixed point f equals that from a straight line S, as d pconstantly equals f1), for the reason repeatedly mentioned-thatis tosay, the said curved line is a parabola.

Fig. 7 is a diagram explaining the use of my invention for trisectingangles. Supposing angle M O N is to be divided into three equal parts, Iprolong side M O of the angle beyond 0 and I draw a circle of any radius0 P,With the center at O intersecting the prolonged angle side at P.Through O, I draw a straight line, forming an angle of forty-fivedegrees with line 0 N and intersecting the said circle at F and'F, and Ifinally draw a circle Z with the center atP and with the radius P P. Theinstrument is then adjusted, as shown in Fig. 3, points f and f beingfixed at F and F, respectively, and pencil p adjusted so as to registerwith point P by releasing the clamping-screw of stud d. After that thesaid screw is clamped again, the instrument thus being adjusted to drawwith the pencil an equilateral hyperbola passing through P. Theinstrument is then actuated to draw the said hyperbola untilintersecting the abovementioned circle Z at It. I then draw a straightline passing through R and P, and

I finally bisect the distance P R at B. If now connecting point B with Oby a straight line, angle B O N will-form the third part of the entireangle M O N to be trisected, and by finally bisecting angle M O B in thewellknown manner the trisection of angle M O N will be performed. Toprove this, it may be observed that by drawing a line 0 Sperpendicularly, directed with respect to line 0 N and prolonging line PR to intersect line 0 N at X and line 0 S atY, the line portions R X andP Y are of the same length, (as a wellknown characteristic of theequilateral hyperbola,) and therefore R Y equals P X, and as angle S O Nis of ninety degrees there will likewise be B X B O, and therefore angleP B O the double of angle B O N. As now P P equals P R, (both beingradii of one and the same circle,) there willlikewise be P O P B, 0being the middle of P P and B the middle of P R. Therefore angle P O Bequals angle P B O-that is to say, angle P O B is likewise the double ofangle B O N, or angle B O N the third part of the entire angle M O N tobe divided.

What I claim as my invention, and desire to secure by Letters Patent,is-

1. An instrument for drawing conic sections, comprising four connectedlinks, a rod adjustably connecting two opposite pivots, means for fixinga thirdpivot, a guide-rod adapted to pass through the fourth pivot,means for fixing one end of said guide-rod, and a pen-carrier adapted toslide on both of said rods, substantially as set forth.

2. An instrument for drawing conic sections, comprising a rhomb composedof links, and a rod adjustably connecting two opposite pivots, aneedle-point for fixing the third pivot, a leg for rigidly holding aguide-rod, and means for connecting the fourth pivot to said leg, and apen or pencil carrier adapted to slide on both of said rods,substantially as set forth.

3. An instrument for drawing conic sections, comprising a variablerhomb, a rod adjustably connecting two pivots at opposite anglesthereof, means for fixing a third pivot, a guide-rod passing through thefourth pivot thereof, means for fixing one end of said guide-rod, and aswiveled pen or pencil carrier adapted to slide on both of said rods,substantially as set forth.

- 4. An instrument for drawing conic sections, comprising a variablerhomb, a rod adapted to be fixed at one pivot and slide through anopposite pivot, means for fixing a third pivot thereof, a guide-rodadjustably connected to the fourth pivot, a support for fixing androtatively mounting at will one end of said rod, and a swiveled pen orpencil carrieradapted to slide on both of said rods, substantially asdescribed.

5. An instrument for drawing conic sections and trisecting angles,consisting of a system of links pivotally connected to each other toform a variable rhomb, a rod passing through a pair of oppositepivot-studs of the rhomb, a pencil-stud or drawing-penmovably mounted onsaid rod, and a guide-rod passing through the pencil-stud and throughone of the other pair of pivot-studs, substantially as set fort-h.

6. An instrument for drawing conic sections, comprising a variablerhomb, a rod rotatably fastened at one pivot and adapted to slide in theopposite one, means for rotatably fixing a third, and a guide-rodadapted to pass through the head of the fourth pivot, a support adaptedto rigidly and at will reiatably fix one end of said rod, means forconnecting said support to the fourth pivot, and a swiveled sliding penor pencil carrier adapted to slide on both of said rods, substantiallyas set forth.

In testimony that I claim the foregoing as my invention I have signed myname in presence of two subscribing witnesses.

\VILHELM ZIETHEN.

Witnesses:

WALDEMAR HAUPT, HENRY HAsPER.

